If-p-is-one-of-roots-from-x-2-2x-6-0-then-p-4-16p-is-equal-to-

Question Number 21733 by Joel577 last updated on 02/Oct/17

If p is one of roots from x^{2} - 2 x + 6 = 0

then p^{4} + 16 p is equal to \dots

Answered by mrW1 last updated on 02/Oct/17

p^{2} - 2 p + 6 = 0

p^{2} = 2 p - 6

p^{4} = {4 p}^{2} - 24 p + 36

p^{4} + 16 p = {4 p}^{2} - 24 p + 36 + 16 p

= {4 p}^{2} - 8 p + 36

= 4 (p^{2} - 2 p + 6) + 12

= 4 \times 0 + 12

= 12

Commented by Joel577 last updated on 02/Oct/17

t h a n k y o u v e r y m u c h

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